Finite Group Databasebeta

← #10782811

Subgroups — #10782811

Order 768.

590 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#81941C211yesmaximal, characteristic, complemented
2#81071C211yesmaximal, characteristic
3#81067C211yesmaximal, characteristic, complemented
4#79527C211yesmaximal, characteristic, complemented
5C3×#1695C211yesmaximal, characteristic, complemented
6#71378C211yesmaximal, characteristic, complemented
7#71134C211yesmaximal, characteristic, complemented
8#71133C211yesmaximal, characteristic, complemented
9#70869C211yesmaximal, characteristic, complemented
10#68548C211yesmaximal, characteristic, complemented
11#68534C211yesmaximal, characteristic, complemented
12#68514C211yesmaximal, characteristic, complemented
13#68513C211yesmaximal, characteristic, complemented
14#68485C211yesmaximal, characteristic, complemented
15D3×#333C211yesmaximal, characteristic, complemented
16#19591—31nomaximal, Sylow
17#5725C2211yescharacteristic
18D3×C4⋊Q8C2211yescharacteristic
19#5557C2211yescharacteristic
20C3×#500C2211yescharacteristic
21C3×#476C2211yescharacteristic
22C3×#476C2211yescharacteristic
23C3×#436C2211yescharacteristic
24#5127—21no—
25#5119—21no—
26#5091C2211yescharacteristic
27#5091C2211yescharacteristic
28#5088C2211yescharacteristic
29#5078C2211yescharacteristic
30#5015C2211yescharacteristic
31D4×C3⋊C8C2211yescharacteristic
32#5008C2211yescharacteristic
33#4890—21no—
34#4890—21no—
35#4882—21no—
36#4882—21no—
37#4871—21no—
38#4864—21no—
39#4862—21no—
40#4856—21no—
41#4850C2211yescharacteristic
42#4848C2211yescharacteristic
43#4835C2211yescharacteristic
44D3×C4⋊C8C2211yescharacteristic
45D3×C4⋊C8C2211yescharacteristic
46#4831C2211yescharacteristic
47#4787—21no—
48#4775—21no—
49#4774—21no—
50#4765—21no—
51#67⋊C8—21no—
52#4720—21no—
53#4694C2211yescharacteristic
54#4685C2211yescharacteristic
55C8×Dic6C2211yescharacteristic
56C3×#334C2211yescharacteristic
57C3×#333C2211yescharacteristic
58C3×#333C2211yescharacteristic
59#4546C2211yescharacteristic
60#4546C2211yescharacteristic
61#4485C2211yescharacteristic
62#4485C2211yescharacteristic
63#4481C2211yescharacteristic
64#4481C2211yescharacteristic
65#4480C2211yescharacteristic
66#4479C2211yescharacteristic
67#4458C2211yescharacteristic
68#3247—31no—
69#3238—31no—
70#3226—31no—
71#2994—31no—
72#1698—31no—
73#1697—31no—
74#1696—31no—
75#1695D311yescharacteristic, complemented
76#1678—31no—
77#1677—31no—
78#1676—31no—
79#1675—31no—
80#1573—31no—
81#1551—31no—
82C2×#333—31no—
83C2×#239—21no—
84C2×D3×Q8—21no—
85C2×C3×M16—21no—
86C3×C4⋊Q8C2311yescharacteristic
87C3×C4⋊Q8C2311yescharacteristic
88C3×C4×D4C2311yescharacteristic
89#947—21no—
90#944—21no—
91#938D411yescharacteristic
92#936D411yescharacteristic
93C2×#213—21no—
94C4×#67—21no—
95#926—21no—
96C22×C3⋊C8—21no—
97C2×#204—21no—
98C2×D3×C8—21no—
99C2×D3×C8—21no—
100#897D411yescharacteristic
101#895—21no—
102#895—21no—
103#893—21no—
104#893—21no—
105D3×C4⋊C4—21no—
106D3×C4⋊C4—21no—
107#890D411yescharacteristic
108#888—21no—
109#888—21no—
110#883—21no—
111#879—21no—
112#874C2311yescharacteristic
113C42×D3C2311yescharacteristic
114#869C2311yescharacteristic
115C4×Dic6C2311yescharacteristic
116C3×#107—21no—
117C3×#107—21no—
118C3×#106—21no—
119C3×#106—21no—
120C3×C4⋊C8C2311yescharacteristic
121C3×C4⋊C8C2311yescharacteristic
122C3×C4⋊C8C2311yescharacteristic
123C3×#102—21no—
124C3×#102—21no—
125C3×C22⋊C8—21no—
126C3×C4×C8C2311yescharacteristic
127#832—21no—
128#830—21no—
129#821—21no—
130#821—21no—
131#821—21no—
132(C2×D3)⋊C8—21no—
133(C2×D3)⋊C8D411yescharacteristic
134(C2×D3)⋊C8D411yescharacteristic
135#818—21no—
136#816—21no—
137#815—21no—
138#815—21no—
139Dic3⋊C8—21no—
140Dic3⋊C8—21no—
141Dic3⋊C8—21no—
142Dic3⋊C8—21no—
143Dic3⋊C8D411yescharacteristic
144Dic3⋊C8D411yescharacteristic
145C8×Dic3—21no—
146#810—21no—
147#810—21no—
148#809—21no—
149#809—21no—
150#809—21no—
151#808—21no—
152#807—21no—
153#807—21no—
154#807—21no—
155#807—21no—
156C4⋊(C3⋊C8)C2311yescharacteristic
157C4⋊(C3⋊C8)C2311yescharacteristic
158C4⋊(C3⋊C8)C2311yescharacteristic
159C4×C3⋊C8C2311yescharacteristic
160#532—31no—
161C2×C4⋊Q8—31no—
162#529—31no—
163#501—61no—
164#500—31no—
165#500C2×D311yescharacteristic
166#489—61no—
167#486—31no—
168#486—31no—
169#483—61no—
170#480—61no—
171#480—61no—
172#480—61no—
173#478—61no—
174#477—31no—
175#477—31no—
176#477—31no—
177#476—31no—
178#476C2×D311yescharacteristic
179#476C2×D311yescharacteristic
180#474—61no—
181#474—61no—
182#466—61no—
183#465—61no—
184#463—61no—
185#460—31no—
186#459—31no—
187#446—31no—
188C8×Q8—31no—
189#436C2×D311yescharacteristic
190#435—61no—
191C8×D4—31no—
192C8×D4—61no—
193#433—61no—
194#432—31no—
195#431—31no—
196#424—61no—
197C2×C4⋊C8—31no—
198C2×C4⋊C8—31no—
199#335—31no—
200#335—31no—
201#334—31no—
202#334C2×D311yescharacteristic
203#333—31no—
204#333—31no—
205#333—31no—
206#333—31no—
207#333C2×D311yescharacteristic
208#333C2×D311yescharacteristic
209#331—31no—
210#331—31no—
211C2×C3×Q8—21no—
212C2×C3×Q8—21no—
213C2×C3×D4C2×D411yescharacteristic
214C22×C3×C4—21no—
215C2×#67—21no—
216#239—82no—
217D3×Q8—82no—
218C2×D12—21no—
219C2×D12—21no—
220C2×D12—21no—
221C2×D12—41no—
222C2×C4×D3—41no—
223C2×C4×D3—41no—
224C2×C4×D3C2×D411yescharacteristic
225C2×C4×D3C2×D411yescharacteristic
226C2×C4×D3#4111yescharacteristic
227C2×Dic6—21no—
228C2×Dic6—41no—
229C2×Dic6C2×D411yescharacteristic
230C3×M16—81no—
231C2×C3×C8—21no—
232C2×C3×C8—21no—
233C2×C3×C8—21no—
234C2×C3×C8C2×D411yescharacteristic
235C2×C3×C8C2×D411yescharacteristic
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4C2×D411yescharacteristic
241C3×C22⋊C4—21no—
242C3×C42C2411yescharacteristic
243#217—21no—
244#217—21no—
245#217—21no—
246#213—81no—
247(C2×D3)⋊C4—21no—
248(C2×D3)⋊C4—41no—
249(C2×D3)⋊C4—41no—
250C4⋊Dic3—21no—
251C4⋊Dic3—21no—
252C4⋊Dic3—21no—
253C4⋊Dic3—21no—
254C4⋊Dic3C2×D411yescharacteristic
255Dic3⋊C4—21no—
256Dic3⋊C4—21no—
257Dic3⋊C4—41no—
258Dic3⋊C4—41no—
259C4×Dic3—21no—
260C4×Dic3C2×D411yescharacteristic
261C4×Dic3C2×D411yescharacteristic
262C4×Dic3#4111yescharacteristic
263C2×C3⋊C8—21no—
264C2×C3⋊C8—21no—
265C2×C3⋊C8—21no—
266C2×C3⋊C8—81no—
267C2×C3⋊C8C2×D411yescharacteristic
268C2×C3⋊C8C2×D411yescharacteristic
269#204—81no—
270D3×C8—81no—
271D3×C8—81no—
272C2×#41—61no—
273C22×Q8—61no—
274C2×SD16—61no—
275C2×D8—61no—
276C2×M16—21no—
277C22×C8—61no—
278C22×C8—61no—
279C22×C8—61no—
280C4⋊Q8—31no—
281C4⋊Q8—61no—
282C4⋊Q8—61no—
283C4⋊Q8—61no—
284C4⋊Q8C22×D311yescharacteristic
285C4⋊Q8C22×D311yescharacteristic
286#127—31no—
287#126—61no—
288#125—31no—
289#124—31no—
290#124—61no—
291#123—61no—
292C22⋊Q8—31no—
293#121—31no—
294#121—61no—
295#121—61no—
296C4×Q8—31no—
297C4×D4—61no—
298C4×D4—61no—
299C4×D4—61no—
300C4×D4C22×D311yescharacteristic
301#117—61no—
302C2×C4⋊C4—61no—
303C2×C4⋊C4—61no—
304C2×C42—31no—
305#107—21no—
306#107—21no—
307#107—61no—
308#107—61no—
309#107—61no—
310#107—61no—
311#107—61no—
312#106—21no—
313#106—21no—
314#106—61no—
315C4⋊C8—31no—
316C4⋊C8—31no—
317C4⋊C8—31no—
318C4⋊C8—31no—
319C4⋊C8—31no—
320C4⋊C8—61no—
321C4⋊C8—61no—
322C4⋊C8—61no—
323C4⋊C8—61no—
324C4⋊C8C22×D311yescharacteristic
325C4⋊C8C22×D311yescharacteristic
326C4⋊C8C22×D311yescharacteristic
327#103—61no—
328#103—61no—
329#103—61no—
330#102—21no—
331#102—21no—
332#102—61no—
333#102—61no—
334#102—61no—
335#102—61no—
336#102—61no—
337#102—61no—
338#102—61no—
339C22⋊C8—21no—
340C22⋊C8—31no—
341C22⋊C8—31no—
342C22⋊C8—61no—
343C22⋊C8—61no—
344#97—61no—
345#97—61no—
346C4×C8—31no—
347C4×C8—61no—
348C4×C8C22×D311yescharacteristic
349C23×C3—21no—
350C22×D3—41no—
351C22×D3#12111yescharacteristic
352C3×Q8—81no—
353C3×Q8—81no—
354C3×D4—21no—
355C3×D4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—41no—
358C2×C3×C4—41no—
359C2×C3×C4—41no—
360C2×C3×C4—41no—
361C2×C3×C4C22×D411yescharacteristic
362C2×C3×C4C22×D411yescharacteristic
363C2×C3×C4C2×#4111yescharacteristic
364#67—42no—
365C2×Dic3—21no—
366C2×Dic3—21no—
367C2×Dic3—41no—
368C2×Dic3#12111yescharacteristic
369C2×Dic3#12111yescharacteristic
370C2×Dic3#12111yescharacteristic
371D12—41no—
372D12—41no—
373D12—41no—
374D12—41no—
375D12—81no—
376D12—82no—
377C4×D3—22no—
378C4×D3—21no—
379C4×D3—21no—
380C4×D3—21no—
381C4×D3—21no—
382C4×D3—82no—
383C4×D3—82no—
384Dic6—21no—
385Dic6—21no—
386Dic6—82no—
387Dic6—81no—
388C3×C8—21no—
389C3×C8—21no—
390C3×C8—41no—
391C3×C8—41no—
392C3×C8—41no—
393C3⋊C8—21no—
394C3⋊C8—21no—
395C3⋊C8—41no—
396C3⋊C8—41no—
397C3⋊C8—41no—
398#41—242no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—31no—
402C2×Q8—61no—
403C2×Q8—121no—
404C2×Q8—242no—
405C2×D4—61no—
406C2×D4—61no—
407C2×D4—61no—
408C2×D4—61no—
409C2×D4—121no—
410C2×D4D3×D411yescharacteristic
411C22×C4—21no—
412C22×C4—31no—
413C22×C4—31no—
414C22×C4—31no—
415C22×C4—121no—
416C22×C4—121no—
417SD16—241no—
418D8—241no—
419M16—81no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—31no—
424C2×C8—31no—
425C2×C8—61no—
426C2×C8—61no—
427C2×C8—61no—
428C2×C8—241no—
429C2×C8—241no—
430C2×C8—241no—
431C2×C8D3×D411yescharacteristic
432C2×C8D3×D411yescharacteristic
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—31no—
438C4⋊C4—61no—
439C4⋊C4—61no—
440C4⋊C4—61no—
441C4⋊C4—61no—
442C4⋊C4—61no—
443C4⋊C4—61no—
444C4⋊C4—121no—
445C4⋊C4—121no—
446C4⋊C4D3×D411yescharacteristic
447C22⋊C4—21no—
448C22⋊C4—61no—
449C22⋊C4—61no—
450C22⋊C4—61no—
451C22⋊C4—61no—
452C22⋊C4—121no—
453C22⋊C4—121no—
454C42—31no—
455C42—31no—
456C42—31no—
457C42—61no—
458C42C23×D311yescharacteristic
459C22×C3—41no—
460C22×C3—41no—
461C22×C3—41no—
462C22×C3C2×#12111yescharacteristic
463C2×D3—21no—
464C2×D3—21no—
465C2×D3—81no—
466C2×D3—81no—
467C2×D3—81no—
468C2×D3#47212yes—
469C3×C4—21no—
470C3×C4—41no—
471C3×C4—81no—
472C3×C4—81no—
473C3×C4#57711yescharacteristic
474C3×C4#57711yescharacteristic
475C3×C4#57811yescharacteristic
476C3×C4#57811yescharacteristic
477Dic3—21no—
478Dic3—21no—
479Dic3—21no—
480Dic3—41no—
481Dic3—41no—
482Dic3—81no—
483C23—21no—
484C23—31no—
485C23—121no—
486Q8—61no—
487Q8—61no—
488Q8—81no—
489Q8—81no—
490Q8—241no—
491Q8—242no—
492D4—21no—
493D4—21no—
494D4—122no—
495D4—121no—
496D4—121no—
497D4—121no—
498D4—121no—
499D4—241no—
500D4—242no—
501C2×C4—21no—
502C2×C4—31no—
503C2×C4—31no—
504C2×C4—31no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—62no—
510C2×C4—61no—
511C2×C4—61no—
512C2×C4—61no—
513C2×C4—61no—
514C2×C4—61no—
515C2×C4—61no—
516C2×C4—121no—
517C2×C4—242no—
518C2×C4—242no—
519C2×C4C2×D3×D411yescharacteristic
520C2×C4C2×D3×D411yescharacteristic
521C2×C4D3×#4111yescharacteristic
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—61no—
528C8—61no—
529C8—121no—
530C8—121no—
531C8—121no—
532C2×C3—81no—
533C2×C3#304611yescharacteristic
534C2×C3#306311yescharacteristic
535C2×C3C2×#47211yescharacteristic
536D3—22no—
537D3—161no—
538C22—32no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—61no—
543C22—61no—
544C22—241no—
545C22—241no—
546C22—241no—
547C22D3×#12111yescharacteristic
548C4—21no—
549C4—41no—
550C4—61no—
551C4—61no—
552C4—61no—
553C4—81no—
554C4—81no—
555C4—121no—
556C4—121no—
557C4—241no—
558C4#576211yescharacteristic
559C4#577811yescharacteristic
560C4#577911yescharacteristic
561C4#577911yescharacteristic
562C3#1959111yescharacteristic, complemented, Sylow
563C2—62no—
564C2—81no—
565C2—481no—
566C2#8043111yescharacteristic
567C2#8090711yescharacteristic
568C2D3×#47211yescharacteristic
subgroupG/H
centerC22D3×#121
commutator, cosocleC3×C42C24
FrattiniC42C23×D3
FittingC3×#1695C2
socleC22×C3C2×#121
prime radical#81071C2
hypercenter#1695D3
hypocenterC3#19591
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #1695

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #81941C2semidirect
3. #81067C2semidirect
4. #79527C2semidirect
5. C3×#1695C2semidirect
6. #71378C2semidirect
7. #71134C2semidirect
8. #71133C2semidirect
9. #70869C2semidirect
10. #68548C2semidirect
11. #68534C2semidirect
12. #68514C2semidirect
13. #68513C2semidirect
14. #68485C2semidirect
15. D3×#333C2semidirect
75. #1695D3semidirect
562. C3#19591semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#819412
#810712
#810672
#795272
C3×#16952
#713782
#711342
#711332
#708692
#685482
#685342
#685142
#685132
#684852
D3×#3332
#195913